Deriving hourly diagnostic surface velocity fields considering inertia and an application in the Yellow Sea

Abstract. Surface currents play an important role in the transport of floating materials in the Yellow Sea, a region strongly influenced by tidal forcing and seasonal wind variability driven by the East Asian monsoon. While diagnostic models have been widely used to estimate surface currents, due to their steady-state assumption, high frequency variations such as tides and inertial oscillations cannot be resolved. To address this limitation, a time-dependent diagnostic model incorporating inertial terms into the governing equations is proposed. The performance of the proposed method is evaluated using buoy and drifter observations from 2015 to 2023. The time-dependent model in this study captures not only low frequency components (geostrophic and Ekman currents) but also high frequency variability (inertial oscillations and tides). Compared to the traditional model assuming steady-state, it shows significant improvement, achieving a correlation of 0.76 and Root-Mean-Square Error of 0.18 m s^-1 (compared to -0.08 and 0.43 m s⁻¹ for the steady model, that caused by wrong governing equation ignoring inertia to describe tides) because of successful consideration of high frequency variability. The decay rate of inertial oscillations is analytically derived, providing insight into the time scale for past signals in surface currents to dissipate. We expect that this study offers a practical framework for surface current estimation considering both high and low frequency signals and can be applied for quick assessments of material transport in other coastal oceans.